Check force on energy

It is common practise to use the potential energy as a collective energy. Some MD codes thus pass the potential energy to PLUMED and PLUMED can then apply forces on this collective variable. We test that any forces that PLUMED applies on the potential energy are correctly passed back to the MD code by doing the following test. We first run a short simulation at $T$ K with a timestep of $\tau$ ps. During the course of this simulation we monitor the potential energy using the following PLUMED input:

Click on the labels of the actions for more information on what each action computes
tested on2.10
tested onmaster
e: ENERGYCalculate the total potential energy of the simulation box. More details
v: VOLUMECalculate the volume the simulation box. More details
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=e,v FILEthe name of the file on which to output these quantities=energy1

We then run a second simulation (starting from identical conditions) at a temperature of $T\alpha$ and with a timestep of $\tau/\sqrt(\alpha)$. The thermostat and barostat relaxation times are similarly divided by $\sqrt(\alpha)$. In the tests that are run on this website we set $\sqrt(\alpha)=1.1$. The PLUMED file above is used when this test is run but a different time series of energy values is recorded as the MD parameters in this second simulation are different.

If PLUMED is working correctly we should be able to recapture the time series of energy values for the first simulation by running an MD simulation with the modified parameters that were used in the second simulation and the following PLUMED input file:

Click on the labels of the actions for more information on what each action computes
tested on2.10
tested onmaster
e: ENERGYCalculate the total potential energy of the simulation box. More details
v: VOLUMECalculate the volume the simulation box. More details
# slope is such that 
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=e FILEthe name of the file on which to output these quantities=energy2
# slope should be (alpha-1)=0.21
RESTRAINTAdds harmonic and/or linear restraints on one or more variables. More details ATthe position of the restraint=0.0 ARGthe values the harmonic restraint acts upon=e SLOPE specifies that the restraint is linear and what the values of the force constants on each of the variables are=0.21

In other words, when forces are passed correctly the time series for the energies and volumes from the first and third of these calculations should be identical.

To determine if PLUMED passes this test we calculate the difference between the time series that were observed in the first and third simulations described above. We then divide this by the difference between the first and second time series.

An NPT version of this calculation is performed as well as an NVT calculation if the virial is passed to PLUMED.

Trajectories

  1. Input and output files for the unpeturbed calculation are available in this zip archive

  2. Input and output files for the peturbed calculation are available in this zip archive

  3. Input and output files for the peturbed calculation in which a PLUMED restraint is used to undo the effect of the changed MD parameters are available in this zip archive

Results

Original With PLUMED Effect of peturbation % Difference
-18174.8223 11.6346 -18174.8223 11.6346 0.0000 0.0000 0.0000 0.0000
-18171.8203 11.6346 -18193.2891 11.6346 6.8730 0.0000 312.3615 0.0000
-18195.1758 11.6475 -18233.7910 11.6321 22.6348 0.0054 170.6014 284.9140
-18169.7109 11.6475 -18286.7832 11.6321 19.0723 0.0054 613.8351 284.9140
-18159.3203 11.6475 -18326.6289 11.6321 22.3125 0.0054 749.8424 284.9140
-18144.0527 11.6475 -18349.8066 11.6321 23.8125 0.0054 864.0584 284.9140
-18128.9961 11.6475 -18356.4980 11.6321 25.3574 0.0054 897.1809 284.9140
-18119.7852 11.6475 -18352.9180 11.6321 28.5508 0.0054 816.5549 284.9140
-18119.5625 11.6475 -18347.0625 11.6321 33.4414 0.0054 680.2944 284.9140
-18127.3613 11.6475 -18344.5020 11.6321 38.2480 0.0054 567.7169 284.9140
-18138.7070 11.6475 -18346.6641 11.6321 40.5703 0.0054 512.5843 284.9140
-18148.4043 11.6475 -18351.8848 11.6321 39.0977 0.0054 520.4416 284.9140
-18154.2266 11.6475 -18358.5195 11.6321 35.6953 0.0054 572.3244 284.9140
-18158.9473 11.6475 -18367.4414 11.6321 34.9492 0.0054 596.5631 284.9140
-18168.3555 11.6475 -18381.4375 11.6321 40.8926 0.0054 521.0775 284.9140
-18186.1172 11.6475 -18401.5371 11.6321 52.7148 0.0054 408.6513 284.9140
-18209.2070 11.6475 -18423.7383 11.6321 63.3301 0.0054 338.7510 284.9140
-18228.7891 11.6475 -18439.8652 11.6321 63.6367 0.0054 331.6893 284.9140
-18235.9199 11.6475 -18442.7617 11.6321 49.5684 0.0054 417.2859 284.9140
-18227.2012 11.6475 -18431.1680 11.6321 25.1816 0.0054 809.9821 284.9140

The table below includes some of the results from the calculation. The columns contain:

  1. Time series for the energy and volume that were obtained from the simulation at $T$ K, $x_{md}$.
  2. Time series for the energy and volume that were obtained from the simulation at $\alpha T$ K and in which PLUMED applied a restraint on the energy, $x_{pl}$.
  3. The absolute value of the difference between the time series of energies and volumes that were obtained from the simulations running at $T$ K and $\alpha T$ K, $\vert x_{md}’-x_{md} \vert$. No PLUMED restraints were applied in either of these simulations.
  4. The values of $100\frac{\vert x_{md} - x_{pl}\vert }{ \vert x_{md}’-x_{md} \vert}$.

If the PLUMED interface is working correctly the first two sets of numbers should be identical and the final column should be filled with zeros.

Graphical representation (beta)

A visualization of the table above:
engvir_v2.10